Abstract:

We introduce FlipMath, a new learning environment for the gentle introduction of problem-solving in mathematics. By means of a simple and intuitive interface (the intended audience are elementary and middle school students), it allows practicing many important activities which help building problem-solving skills:

- Text analysis of the problem, with the recognition of the problem situation, the selection of relevant data and the identification of expected results;
- The graphic composition (in a flow-chart style) of a resolution algorithm (using drag-and-drop operations) that combines the selected data to obtain the expected results;

The program, developed with JavaFX, is made of two interacting components: the student’s working environment and the teacher’s authoring one.
The student’s working environment provides immediate feedbacks carrying out all calculations automatically; it is able to assess the correctness of the student’s solution beyond the simple numerical equality (which may be fortuitous). This is achieved using jscl-meditor, an open-source symbolic computational engine written in Java, and inspecting the algebraic expression obtained by the computation tree.
The teacher’s authoring environment allows the definition of new problems, tagging the parts of the text which are required to accomplish the student’s task. It also allows the full monitoring of pupil’s activities.

References:
[1] Tarsia A., “Un Ambiente Didattico per l’Avvio al Problem-Solving in Matematica”, Bachelor’s thesis in Computer Science, Pisa (Italy), 2012.
[2] Rimoldi H.J.A., Problem Solving as a Process, Educational and Psychological Measurement, Vol. 20, No. 3, (1960).
[3] R. Zan, Problemi e convinzioni, Bologna, Pitagora editrice, (1988).

Keywords:

Problem-solving, Learning environments, Computer-aided learning, Automatic assessment.